Thomas Mueller netted twice, while goals by Robert Lewandowski, David Alaba and Arjen Robben saw Pep Guardiola’s Bayern emphatically avenge their 2-0 defeat at the Emirates Stadium a fortnight ago, their only loss of the season.

“That was a key game for us, otherwise we would have had a lot of work to do in the group,” Mueller told German television’s ZDF.

“If we win our next game now, we should be through, so tonight was a big step.”

France striker Oliver Giroud scored Arsenal’s consolation goal with 20 minutes left, but between them Mueller and Lewandowski have now scored 31 goals for Bayern in all competitions this season.

This was Arsenal’s joint heaviest away defeat in Europe, equalling the 4-0 drubbing at AC Milan in the last 16 in February 2012.

With two games left, Arsene Wenger’s side have only a mathematical chance of reaching the knock-out phase after Dinamo Zagreb’s 2-1 defeat at Olympiakos.

The Gunners have three points along with Dinamo, while Olympiakos and Bayern both have nine with the Germans top of Group F on goal difference.

“We have to win both games and get two goals on Olympiakos, but it’s not over and that’s how we have to approach it,” said Arsenal defender Per Mertesacker.

Arsenal next host Dinamo in a fortnight, then play Olympiakos away in their final game.

“We need to bounce back and put away negative energy,” he said.

Meanwhile, Willian produced a brilliant free kick to give Chelsea a crucial 2-1 win over Dynamo Kiev, easing the pressure on troubled manager Jose Mourinho.

Mourinho’s tenuous hold on his job appeared to be loosening even further when Dynamo’s Aleksandar Dragovic cancelled out his first half own goal with a late equaliser for the Ukrainian champions.

But with just seven minutes remaining at Stamford Bridge, Brazilian winger Willian whipped a sensational 30-yard free-kick into the top corner to give Chelsea just their second win in their last nine games in all competitions.

Failure to beat Dynamo would have left the struggling English champions in severe danger of failing to make the last 16, but Willian’s heroics lifted them to second place in Group G and put qualification back in their own hands with fixtures against Maccabi Tel Aviv and Porto remaining.

Chelsea were still well below their best, yet the result will buy Mourinho time to work on resolving the crisis that threatens to bring a premature end to his second spell at the club.

“The win is a big relief. The players deserve to get compensation for their hard work,” Mourinho said.

“Many players are coming to their normal levels, despite having feelings as a team when negative moments come.

“The difference today was we had confidence in the negative moment.

“The team was strong mentally, they kept trying and I’m happy with that.”

Amid all the talk of a dressing room mutiny from a group of players unhappy at his stern man-management, the Portuguese coach continues to insist he won’t be sacked and captain John Terry leapt to his defence yesterday in passionate fashion.

But it was deeds rather than words that would define the remaining days of Mourinho’s reign and he made a big statement by dropping Eden Hazard after another poor display in Saturday’s loss against Liverpool.

Chelsea quickly seized the initiative and Willian was a constant menace on the right flank, but when he whipped over a teasing cross no Chelsea player was alert enough to convert the chance, triggering an anguished cry from Mourinho.

Like most of his team-mates Diego Costa has been painfully short of his best this year and he shot wildly over when the ball fell to him inside the penalty area.

But Mourinho’s luck changed for the better in the 34th minute as Chelsea took the lead in fortuitous circumstances when Dragovic headed past Olexandr Shovkovskiy into his own net.

However, Dragovic made amends when he beat Asmir Begovic for a 78th minute equaliser that stunned the Stamford Bridge faithful.

But Willian came to the rescue in spectacular fashion in the 81st minute when he curled his free-kick into the top corner to spark wild celebrations in the stands and a sigh of relief from Mourinho.